No, it really is in the gas pressure at muzzle exit. A smaller cartridge or a longer barrel simply has a lower pressure report. That equals a quieter report. A 300 Savage goes "blam" compared to a 308 that goes "BANG", as one example.
Burn rate of the powder is also a factor, but the myth that some powders are still burning as the bullet exits is just that: a myth. The turth is that a faster powder will have a lower residual pressure at bullet exit. Lower velocity, too, but that's another issue.
